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A: To Determine: nth taylor polynomial for fx=ex at x=0
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- 4. Let the function x(1) be given by the conditions x (0) = 1 and x (1) = 1x(1) + 2[x(1)]² Determine the second order Taylor polynomial for x(1) about / == = 0. 5. Establish the approximationThe Taylor polynomial of order 2 generatedby a twice-differentiable function ƒ(x) at x = a is called thequadratic approximation of ƒ at x = a., find the(a) linearization (Taylor polynomial of order 1) and (b) quadraticapproximation of ƒ at x = 0. ƒ(x) = ln (cos x)Let f(x)=8x+2ln(x). Find a second degree Taylor polynomial about c=1 and use P2(x) to approximate 16+2ln(2) with determining a bound for the error of the approximation.
- Express the 4th Taylor polynomial of the function f (x) = e3x at the neighborhood a = 1.Let f(x) = cos(2x)(a) Compute p2(x) (the second order Taylor polynomial) at a = π/8.(b) For the function in part (a), use the Taylor estimation theorem to find an upper bound for theapproximation error|R2(x)| = |f(x) − p2(x)|if x lies in the interval [0, π/4]let f(x) = cos(x) and x0 = 0. Find the Taylor polynomial of degree N = 4.
- The Taylor polynomial of order 2 generatedby a twice-differentiable function ƒ(x) at x = a is called thequadratic approximation of ƒ at x = a., find the(a) linearization (Taylor polynomial of order 1) and (b) quadraticapproximation of ƒ at x = 0. ƒ(x) = esin x1. determine the second-order Taylor approximation of the polynomial p(x) = x^5 + 6x^4 + x^2 − 1 at the points x = 0 and x = 1.Calculate the Taylor polynomial T3 centered at x = a for the given function and values of a andEstimate the accuracy of the 3th degree Taylor approximation, f(x) ≈T3(x), centered at x = a onthe given interval. 2) f(x) = ln(1 + 2x), a = 1, and [0.5,1.5]